The crystal structure parameters and magnetic and electrical properties of La1−x CaxMnO3−x/2 reduced manganites with 0≤x≤0.5 are established. These investigations contribute to the understanding of magnetic interactions in manganites without Mn4+ ions. It is found that these manganites show a long-range antiferromagnetic order up to x=0.09 and transform into spin glasses at 0.09<x≤0.35. The compositions in the range 0.35<x≤0.5 show a strong increase in the spontaneous magnetization and critical point associated with the appearance of spontaneous magnetization and can therefore be viewed as inhomogenious ferromagnets. The magnetic and crystal structure peculiarities of La0.5Ca0.5MnO2.75 are established by the neutron diffraction method. The strongly reduced samples show a large magnetoresistance below the point where the spontaneous magnetization develops. The magnetic phase diagram of La1−x CaxMnO3−x/2 is established by magnetization measurements. The magnetic behavior is interpreted assuming that the Mn3+-O-Mn3+ magnetic interaction is anisotropic (positive-negative) in the orbitally ordered phase and isotropic (positive) in the orbitally disordered phase. Introduction of the oxygen vacancies changes the magnetic interaction sign from positive to negative, thereby leading to a spin glass state in strongly reduced compounds. The results obtained reveal unusual features of strongly reduced manganites such as a large ferromagnetic component, a high magnetic ordering temperature, and a large magnetoresistance despite the absence of Mn3+-Mn4+ pairs. In order to explain these results, the oxygen vacancies are supposed to be ordered.